Today, Tony the Alpaca needs some help with an array he found in the grass!

Tony gives you an array ~a~ of length ~N~. He has ~Q~ queries to ask you about the array. Each query is of the form ~l_i~, ~r_i~, ~x_i~, such that ~l_i \le r_i~.

Given these parameters, Tony wants to know if there are ~2~ distinct indices ~p~ and ~q~ between ~l_i~ and ~r_i~ inclusive such that ~a_p \cdot a_q = x_i~.

Also, since Tony hates numbers that are the same, ~a_p~ must not be equal to ~a_q~. To keep Tony happy, you must answer all his queries!

Constraints

~1 \le N \le 10^6~

~1 \le Q \le 5 \cdot 10^4~

~1 \le a_i \le 10^5~

~1 \le l_i \le r_i \le N~

~1 \le x_i \le 10^5~

Subtask 1 [10%]

~1 \le N, Q, a_i \le 10^3~

Subtask 2 [90%]

No additional constraints.

Input Specification

The first line of input contains two integers ~N~ and ~Q~.

The second line of input contains ~N~ integers ~a_i~.

The final ~Q~ lines will each contain ~l_i, r_i, x_i~, the parameters for the ~i^{th}~ query.

Output Specification

For each query, output YES if there are two distinct indices that multiply to ~x_i~, and NO otherwise.

Sample Input 1

5 3
1 5 5 2 3
1 3 25
1 4 6
1 5 10

Sample Output 1

NO
NO
YES

Sample Input 2

6 4
2 4 2 4 2 4
1 3 8
1 6 5
1 2 1
1 5 16

Sample Output 2

YES
NO
NO
NO